Numerical Evaluation of Transport Phenomena in a T-junction

ARTICLE pubs.acs.org/IECR

Numerical Evaluation of Transport Phenomena in a T-junction Microreactor with Coils of Different Configurations Agus P. Sasmito,*,†,‡ Jundika C. Kurnia,† and Arun S. Mujumdar†,‡ †

Department of Mechanical Engineering and ‡Minerals Metals Materials Technology Center, National University of Singapore, 9 Engineering Drive 1, Singapore 117576 ABSTRACT: Microchannel T-junction configuration is used in chemical processing for passive mixing and reactions, because of its relatively easy control of the reaction environment. However, poor mixing and low reaction rate are some of the main drawbacks of this design. This study proposes mass-transport enhancement in a microchannel T-junction by utilizing various configurations of coiled base channel design (e.g., conical spiral, in-plane (flat) spiral, and helical spiral coils). Their mass-transport performance is investigated numerically and compared with that of the conventional straight microchannel T-junction. Laminar flow of gas flow with reactions is investigated using a three-dimensional computational fluid dynamics (CFD) model. Four different microchannel designs, three different channel Reynolds numbers, and three different helical coil diameters are investigated. The coils are made of a square cross-section tube. The results indicate that the coiled base channel displays improved mixing and conversion rate of the reactant. Finally, advantages and limitations of each design are discussed in the light of present numerical results.

1. INTRODUCTION Over the past decade, microreactors and micromixers have gained considerable attention, especially in the chemical processes and pharmaceutical industries, because of their higher transport rates, safer environment for highly exothermic or explosive chemical reactions, compact design, and simpler process control. Microchannel T-junction design is widely used for passive mixing processes, because it is easily manufactured and does not require additional energy or mechanical devices for mixing; however, since small scale mixing depends mainly on molecular diffusion, a relatively long channel is necessary to achieve the desired mixing. Numerous experimental and numerical investigations18 on mixing processes in a microchannel T-junction have been conducted and reported. Extensive reviews on the mixing processes in microchannel have also been published.9,10 To enhance mixing, various approaches have been introduced (e.g., the introduction of mechanical, magnetic, acoustic, thermal, or electrical disturbances). Most impose a requirement of additional external energy. In a previous study in our group, Wang et al.11 investigated mixing in laminar confined impinging streams and proposed the addition of fins inside the channel to improve mixing without additional external energy input; however, it imposes a higher pressure drop and manufacturing cost. Thus, there is a need for an improved, yet easy-to-manufacture, design for mixing in a microchannel T-junction. Coiled tubes are known as a passive heat- and mass-transfer enhancement, because of the presence of secondary flows induced by coil curvature. Their compact design, higher heat- and mass-transfer rate, and ease of manufacture are some of the main advantageous of coils. Aside from their industrial application, transport phenomena in coils have also attracted much attention from researchers. Several experimental1215 and numerical studies1625 have been reported, along with reviews of flow and heat-transfer characteristics.26,27 Jones et al.25 numerically investigated mixing enhancement in a twisted pipe, called chaotic advection; they showed the enhanced r 2011 American Chemical Society

longitudinal particle dispersal because of the coupling between chaos in the transverse direction and the nonuniform longitudinal transport of paticles. In our previous works,1619 various coils tube designs were simulated to investigate heat-transfer enhancement, relative to the straight tube. Kurnia et al.18 compared heat-transfer performance of in-plane coiled tube with various cross-section geometries, e.g. square, rectangular, trapezoidal, half-circle, and triangular. It was found that coils with a square cross-section yields relatively higher heat-transfer performance, compared to other designs, because of the presence of secondary flow in the tube corner and curvature geometry. In the chemical reactor field, Agrawal and Nigam28 simulated coiled tubular chemical reactor tubes with a circular cross section, employing first-order reaction kinetics and considering the premix inlet condition. They found that the performance of coiled chemical reactor lies between that of plug and laminar tube flow reactors. Kumar et al.29 modeled mixing processes of two miscible liquids in a horizontal curved tube. They prescribed the inlet concentrations of 0 and 1 in the two halves of the duct perpendicular to the plane of curvature without considering the opposing stream in a T-junction and without chemical reactions. Their results suggest that mixing is much improved, compared to that of a straight tube of the same length. Recently, Nigam and his co-workers3032 proposed a coils flow inverter design and observed that the heat transfer and mixing rate improves significantly, compared to the conventional designs. As stated previously, both the microchannel T-junction and coiled tube offers various advantages. Here, we propose a novel Special Issue: Nigam Issue Received: January 20, 2011 Accepted: May 26, 2011 Revised: May 25, 2011 Published: May 26, 2011 1970

dx.doi.org/10.1021/ie200139s | Ind. Eng. Chem. Res. 2012, 51, 1970–1980

Industrial & Engineering Chemistry Research

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Figure 1. Schematic representation of microchannel T-junction with (a) straight, (b) conical spiral, (c) in-plane spiral, and (d) helical spiral channels.

Figure 2. Geometrical details of microchannel T-junction (front view, T-junction is not included) with (a) straight, (b) conical spiral, (c) in-plane spiral, and (d) helical spiral channels.

combination of the microchannel T-junction with a coiled design made of square cross section to further improve mixing and reaction rate. Note that the square cross-section geometry was chosen because it has higher heat-transfer performance (compared to other designs),18 it is relatively easy to manufacture, and, for the same cross-sectional area, the total catalytic surface area of square crosssection channel is slightly higher than that of the circular crosssection. To the best of our knowledge, no prior study has been reported that examined simultaneous mixing and reactions in a microchannel T junction coupled with various coiled channel configurations. Therefore, the objectives of the work presented here are 3-fold: (i) to evaluate mixing and reaction rate performance of various configurations of microchannel T-junctions with coiled of square cross section (e.g., conical spiral, in-plane spiral, and helical spiral coils), relative to the straight microchannel T-junction; (ii) to study the effect of inlet channel Reynolds number on mixing and reaction kinetics; and (iii) to evaluate the impact of coil diameter to the mixing and reaction rate performance. The layout of the paper is as follows. First, the mathematical model is introduced; it comprises conservation equations of mass, momentum, species, and energy. The surface reaction of methane oxidation over a platinum surface is chosen as an example to demonstrate the concept, because of its well-known reaction kinetics.3337 The mathematical model is then solved numerically utilizing finitevolume-based CFD software Fluent 6.3.26. Fluid flow, heat and mass transfer performance of various coiled designs is evaluated in terms of a “Figure of Merit”, which is defined later. Parametric studies are then carried out for the effect of inlet channel Reynolds number and helical coils diameter. Finally, advantages and limitations of the design are highlighted, and conclusions are drawn based on the results presented.

Figure 1); whereas air flows from the left inlet (green arrow in Figure 1). Methane and air mix in the opposing streams in a T-junction and react at the surface of the channel wall. The reactions at the channel wall comprise multistep reactions including adsorption reaction, surface reaction, and desorption reaction. The surface species are calculated from site balance equations, while the surface reactions create sources of bulk phase, which determine their deposition rate on the surface. The flow is assumed to be steady, laminar, and Newtonian. The miscible species mixture follows the ideal gas law. Furthermore, to ensure fidelity of the comparison of mixing and reaction performance for each T-junction design, the total length of each channel (L) is held constant (see Figure 2 for details of the geometries). Since this work relates only to laminar flow, a precise numerical solution is adequate to simulate the reality very closely. 2.1. Governing Equations. The conservation equations of mass, momentum, species, and energy are given by

2. MATHEMATICAL MODEL The physical model (see Figure 1) is comprised of four microchannel T-junction designs (e.g., straight T-junction, conical spiral T-junction, in-plane spiral T-junction, and helical spiral T-junction). All channels are of square cross-section. We assume that methane gas enters the channel from the right inlet (red arrow in

r 3 Fu ¼ 0

ð1Þ

2 T r 3 Fu X u ¼ rp þ r 3 ½μðru þ ðruÞ Þ μðr 3 uÞI 3 ð2Þ r 3 ðFuωi Þ ¼ r 3 ðFDi rωi Þ þ Ri, gas

ð3Þ

r 3 ðFcp uTÞ ¼ r 3 ðkeff rTÞ þ Stemp

ð4Þ

In the above equations, F is the fluid density, u the fluid velocity, p the pressure, μ the dynamic viscosity, ωi the mass fraction of species i, Di the diffusion coefficient of species i, Ri the mass consumed or produced by the reactions, cp the specific heat of the gas mixture, T the temperature, keff the effective thermal conductivity, and Stemp is the heat released/absorbed due to reaction. 2.2. Chemical Reactions. Here, we consider as an example case of mixing and heterogeneous reaction of methane oxidation at the microchannel surface coated with a platinum catalyst.3337 Note that other types of mixing and reaction processes can also 1971

dx.doi.org/10.1021/ie200139s |Ind. Eng. Chem. Res. 2012, 51, 1970–1980


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i is given by

Table 1. Surface Reaction Mechanism βr

Ar

No.

reaction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

H2 þ 2Pt(s) f 2H(s) 2H(s) f H2 þ 2Pt(s) O2 þ 2Pt(s) f 2O(s) O2 þ 2PT(s) f 2O(s) 2O(s) f O2 þ 2Pt(s) H2O þ Pt(s) f H2O(s) H2O(s) f H2O þ Pt(s) OH þ Pt(s) f OH(s) OH(s) f OH þ Pt(s) H(s) þ O(s) f OH(s) þ Pt(s) H(s) þ OH(s) => H2O(s) þ Pt(s) OH(s) þ OH(s) f H2O(s) þ O(s) CO þ Pt(s) f CO(s) CO(s) f CO þ Pt(s) CO2(s) f CO2 þ Pt(s) CO(s) þ O(s) f CO2(s) þ Pt(s) CH4 þ 2Pt(s) f CH3(s) þ H(s) CH3(s) þ Pt(s) f CH2(s) þ H(s) CH2(s) þ Pt(s) f CH(s) þ H(s) CH(s) þ Pt(s) f C(s) þ H(s) C(s) þ O(s) f CO(s) þ Pt(s) CO(s) þ Pt(s) f C(s) þ O(s) OH(s) þ Pt(s) f H(s) þ O(s) H2O(s) þ Pt(s) f H(s) þ OH(s) H2O(s) þ O(s) f OH(s) þ OH(s)

4.36 10 0.5 3.7 1020 0 17 1.8 10 0.5 2.01 1014 0.5 3.7 1020 0 2.37 108 0.5 1 1013 0 3.25 108 0.5 1 1013 0 3.7 1020 0 3.7 1020 0 3.7 1020 0 7.85 1015 0.5 13 1 10 0 1 1013 0 3.7 1020 0 2.3 1016 0.5 3.7 1020 0 3.7 1020 0 3.7 1020 0 3.7 1020 0 17 1 10 0 1.56 1018 0 1.88 1018 0 4.45 1020 0 7

Er (J/kmol) 0 6.74 107 0 0 2.13 108 0 4.03 107 0 1.93 108 1.15 107 1.74 107 4.82 107 0 1.25 108 2.05 107 1.05 108 0 2 107 2 107 2 107 6.28 107 1.84 108 1.15 107 1.74 107 4.82 107

be simulated within the framework of the model derived here if their kinetics are known. The model treats chemical species deposited on surfaces as being distinct from the same chemical species in the gas. Similarly, reactions involving surface deposition are defined as distinct surface reactions and hence treated differently from bulk phase reactions involving the same species. Seven gas species (CH4, O2, H2, H2O, CO, CO2 and N2), one bulk/solid species (Pt(b)), and 11 surface species (e.g., H(s), Pt(s), O(s), OH(s), H2O(s), CH3(s), CH2(s), CH(s), C(s), CO(s), CO2(s)) that describe the coverage of the surface with adsorbed species are included in the model. The detailed multistep reaction mechanism and its reaction rate constants are listed in Table 1. The gas-phase species and surface species can be produced and depleted by surface reaction; hence, it is written in a general form as Ng

Nb

Ns

þ

Nb

Ns

b00i, r Bi þ ∑ s00i, r Si ∑ i¼1 i¼1

Ng Y gi,0 r s0i, r ½Gi wall ½Si wall

^ i, site ¼ R

ðgi,00r gi,0 r ÞR r ∑ r¼1 Nrxn

∑ ðb00i, r b0i, r ÞR r

i ¼ 1, 2, 3, :::, Ng

ði ¼ 1, 2, 3, :::, Nb Þ

r¼1 Nrxn

∑ ðs00i, r s0i, r ÞR r

ði ¼ 1, 2, 3, :::, Ns Þ

r¼1

ð7Þ

while the reaction rate constant is computed using the Arrhenius expression, which is given by kf , r

Er ¼ Ar T exp RT βr

ð8Þ

On the reacting wall surface, it is assumed that the mass flux of each gas species is balanced with its rate of production/consumption, which is given by Fwall Di

Dωi, wall ^ i, gas m_ ωi, wall ¼ Mw, i R Dn dep

i ¼ 1, 2, 3, :::, Ng

ð9Þ D½Si wall ^ i, site ¼R Dt

ði ¼ 1, 2, 3, :::, Ns Þ

ð10Þ

The gas concentration at the wall is calculated from the species mass fraction, which is defined as ½Gi wall ¼

Fwall ωi, wall Mw, i

ð11Þ

while m_ dep is the net rate of mass deposition or etching as a result of surface reaction, which is given by m_ dep ¼

Nb

∑ Mw, i R^ i, bulk i¼1

½Si wall ¼ Fsite zi

ð5Þ

where Gi, Bi, and Si represents the gas-phase species, the solid species, and the surface-adsorbed species, respectively. In addition, g0 , b0 , and s0 are the stoichiometric coefficients for each reactant species; g00 , b00 , and s00 are stoichiometric coefficients for each product species; and Kr is the overall reaction rate constant. Since only the species involved as reactants or products will have a nonzero stoichiometric coefficient, the rate of reaction is calculated as R r ¼ kf, r

^ i, bulk ¼ R

Nrxn

ð12Þ

[Si]wall is the site species concentration at the wall, and is defined as

Ng

∑ gi,0 r Gi þ i∑¼ 1 b0i, r Bi þ i∑¼ 1 s0i, r Si sfrs i∑¼ 1 gi,00r Gi i¼1 Kr

^ i, gas ¼ R

ð13Þ

where Fsite is the site density of the catalyst and zi is the site coverage of species i. 2.3. Constitutive Relations. The gas density is given by the ideal gas law: F¼

pM RT

ð14Þ

where R is the universal gas constant and M denotes the mixture molecular weight given by

ð6Þ M ¼

i¼1

where [Gi]wall represents molar concentration on the wall. Thus, the net molar rate of production or consumption of each species

ωCH4 ωH2 ωO2 ωH2 O ωCO2 ωCO ωN2 þ þ þ þ þ þ MCH4 MH2 MO2 MH2 O MCO2 MCO MN2

!1

ð15Þ 1972



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The gas mixture viscosity (μ) is defined as38 μ¼

x μ

∑R ∑ xRβ ΦRR, β

ðR, β ¼ CH4 , H2 , O2 , H2 O, CO, CO2 , N2 Þ

β

ð16Þ where xR,β are the mole fractions of species R and β, and 2 32 0 11=2 !1=2 1=4 ðgÞ Mβ 1 MR μR 6 7 ΦR, β ¼ pffiffiffi 1 þ 41 þ @ ðgÞ A 5 ð17Þ Mβ M 8 R μβ 38

The multicomponent gas mixture thermal conductivity is defined by keff ¼

∑ki ωi

ð18Þ

while the gas mixture specific heat capacity (cp) is evaluated using cp ¼

∑i ωi cp, i

ð19Þ

The results are discussed later in term of a figure of merit, a mixed mean mass fraction, and temperature. The figure of merit (FoM) is used to evaluate the effectiveness of the mixing and reaction rate in the microchannel T-junction. It is defined as the ratio of reactant conversion rate per unit pumping power required:

Figure 3. Validation with experimental data by Bond et al.,36 and comparison with numerical results by Bond et al.36 and Canu37 at low and high inlet stoichiometry.

Table 2. Base-Case Conditions and Geometrical Parameters

out

FoM ¼

m_ ini, mean m_ i, mean Ppump

ð20Þ

where Ppump is the pumping power required to drive flow through the channel, which is given by ! 1 Ppump ¼ Q_ Δp ð21Þ ηpump Here, ηpump is the pump efficiency (assumed to be 70%), Q the volume flow rate, and Δp the pressure drop. The mixed mean temperature is given by Z 1 Tu dAc ð22Þ Tmean ¼ VAc Ac while the mixed mean mass fraction is written as Z 1 ωi, mean ¼ ωi u dAc VAc Ac

ð23Þ

parameter

value

L Rpi Rpo Rci Rco Rh pout Pt(s) s Tin air Tin fuel Twall Uin air Uin fuel ωin CH4 ωin O2 W

120 103 m 2 103 m 9 103 m 2 103 m 9 103 m 4 103 m 101 325 Pa 2.7063 108 kg mol m2 1 103 m 300 K 300 K 1290 K 1, 5, 10 m s1 1, 5, 10 m s1 0.9 0.21 1 103 m

2.4. Boundary Conditions. The boundary conditions for the flow inside the microchannel T-junction are as follows: • Left inlet: oxidant flow is introduced to the channel; we prescribe the inlet velocity, inlet temperature, and species mass fraction, which represent typical ambient air conditions. in T ¼ Tair ,

in , u ¼ Uair

where Ac is the cross-sectional area of the channel, and V is the mean velocity, which is given by Z 1 V ¼ u dAc ð24Þ A c Ac

ωO2 ¼ ωin O2 ,

ωN2 ¼ 1 ωin O2

ð27Þ

• Right inlet: gaseous fuels (methane and hydrogen) enter the channel; a constant inlet velocity, temperature, and species mass fraction are prescribed.

As a measure of the degree of mixing, we compare the standard deviation of concentration distribution at the cross-sectional area along the channel, which is defined by Z 1 σstd ¼ ðωi ωi, ave Þ2 dAc ð25Þ A c Ac

in u ¼ Ufuel ,

in T ¼ Tfuel ,

ωCH4 ¼ ωin CH4 ,

ωH2 ¼ 1 ωin CH4

ð28Þ

• Outlet: we specify the pressure- and stream-wise gradient of the temperature and the species mass fraction is set to zero. The velocity is not known a priori but must be iterated from the neighboring computational cells.

where ωi,ave is the average concentration at the cross-sectional area, which is given by Z 1 ωi, ave ¼ ωi dAc ð26Þ A c Ac

p ¼ pout , 1973

n 3 rT ¼ n 3 rωi ¼ 0

ð29Þ



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Figure 4. Velocity contours and vectors in microchannel T-junction cross section at L = 50 mm for (a) straight, (b) conical spiral, (c) in-plane spiral, and (d) helical spiral channels.

• At the nonreacting walls: we specify no slip condition, no species flux, and the adiabatic conditions at the channel wall before the T-junction. u ¼ 0,

rωi ¼ rT ¼ 0

ð30Þ

• At the reacting walls: at the channel walls after the T-junction, the surface reaction is taken into account and is resolved according to eq 9. In addition, we prescribe no slip condition and a constant wall temperature. u ¼ 0,

T ¼ Twall

ð31Þ

3. SOLUTION PROCEDURES The computational domains (see Figure 1) were created in AutoCAD 2010; the commercial preprocessor software Gambit 2.3.16 was used for meshing and labeling boundary conditions, and to determine the computational domain. Three different mesh designs—2.5 105, 5 105, and 1 106—were implemented and compared in terms of the local pressure, velocity, species mass fraction, and temperature to ensure a mesh-independent solution. We found that the mesh numbers at ∼5 105 give an ∼1% deviation, compared to a much-finer mesh size of 1 106; however, the results from the mesh size of 2.5 105 deviate up to 10%, compared to those from the finest mesh design. Therefore, a mesh

consisting of ∼5 105 elements was found to be sufficient for the numerical experiments: a fine structured mesh was used near the wall to resolve the boundary layer and an increasingly coarser mesh in the middle of the channel, in order to reduce the computational cost. Equations 14, together with appropriate boundary conditions and constitutive relations, which are comprised of 11 dependent variables—p, u, v, w, ωO2, ωCH4, ωH2, ωH2O, ωCO2, ωCO, and T—were solved using the finite-volume solver Fluent 6.3.26. Gas properties and reaction mechanisms were defined using ChemKIN software; user-defined functions (UDF) were written in C-language, to account for the temperature dependence of the thermophysical properties of the fluid. The equations were solved with the well-known SemiImplicit Pressure-Linked Equation (SIMPLE) algorithm, first-order upwind discretization, and the Algebraic Multigrid (AMG) method. As an indication of the computational cost, it is noted that, on average, ∼5001000 iterations are needed for convergence criteria for all relative residuals of 106; this takes 23 h on a workstation with a quad-core processor (1.83 GHz) and 4 GB of RAM.

4. RESULTS AND DISCUSSION The numerical simulations were carried out for typical conditions found in microchannel T-junctions; the base-case conditions, 1974



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Figure 5. Oxygen mass fraction distributions in microchannel T-junction cross section at L = 50 mm for (a) straight, (b) conical spiral, (c) in-plane spiral, and (d) helical spiral channels.

together with the physical parameters and geometric parameters, are listed in Table 2. In the following, four different channel designs, three different inlet flow rates, and three different helical coil diameters are simulated to study the impact of these factors on mass-transport enhancement. 4.1. Validation. When developing and implementing mathematical model to predict the behavior of mixing and reactions, one must pay special attention to validation of the model, because of the inherent complexity of coupled physical phenomena and the interaction between mixing species and its corresponding kinetics. In this work, we intend to validate our model with an experimental methane catalytic oxidation by Bond et al.36 The methane conversion rate in monolithic reactor was approximated as a repeating single channel flow (see Bond et al. 36 for details of the experimental setup). The results were also compared with simulation data from Bond et al.36 and Canu.37 The validation is initiated with methane catalytic oxidation at low stoiciometry gas inlet (ξ = 0.18), after which the methane conversion rate of higher inlet stoichiometry (ξ = 0.39) is compared, as depicted in Figure 3. It is found that the model

predictions agree well with the methane conversion rate from the experimental counterpart at both low and high inlet stoichiometry. In addition, the present model has better agreement, compared to the model prediction by Bond et al.36 and Canu,37 especially at high methane stoichiometry. This implies that the model correctly accounts for the fundamental physics associated with the reactions. 4.2. Effect of Geometry. One of the key factors that determine the mixing and reaction performance is the geometric design of the channel. This study examines four different microchannel T-junction geometries: straight, conical spiral, in-plane spiral, and helical spiral. Since the mixing and reaction rates are directly linked to the flow behavior, it is of interest to investigate the flow patterns inside the tubes. Our previous work on coils of square tubes1619 showed that the presence of centrifugal force due to curvature leads to significant radial pressure gradients in the flow core region. In the proximity of the inner and outer walls of the coils, however, the axial velocity and the centrifugal force each approach zero. Hence, to balance the momentum transport, secondary flow should develop along the outer wall. This, indeed, is the case, as can be seen in Figure 4, where the secondary flows present in the coiled tube with 1975



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Figure 6. Methane mass fraction distributions in microchannel T-junction cross section at L = 50 mm for (a) straight, (b) conical spiral, (c) in-plane spiral, and (d) helical spiral channels.

higher velocities is generated in the outer wall region of the coils (see Figures 4bd). However, this is not the case for the straight T-junction, because a fully developed flow exists inside the channel. It is noted that, at this particular inlet Reynolds number (Re ≈ 500, where Re = FUDh/μ), the secondary flows appear as two pairs in all coiled designs. We note that the vortices of secondary flows for the in-plane spiral channel appear as a pair in the middle of the channel; for the helical and conical channels, the vortices occur toward the upper and lower corners of the channel (see velocity vector in Figure 4). The presence of secondary flow with higher velocities toward the outer wall of the coiled channel is expected to have a direct impact on the mixing and reaction characteristics. This can be inferred from Figures 5 and 6, which present the local mass fraction distribution of oxygen and methane, respectively, over the cross sections of various channel designs. Here, several features are apparent; foremost is that coiled tubes yield a significantly higher conversion rate, which is represented by lower oxygen and methane mass fractions than those for a straight-channel T-junction. Moreover, more-uniform mass-fraction distributions are observed for the coiled tube than for the

straight channel, which means that both reactants are mixed well. For the straight-channel T-junction, on the other hand, the higher oxygen concentration located at the left side of the channel and methane concentrates at the right side of the channel means that oxygen and methane are not mixed perfectly. It is also worth noting that the helical channel performs the best, in terms of conversion rate among all coiled channels. Looking further into mixing, reaction, and heat-transfer performance along the channel (see Figure 7), note that the coiled tubes have superior performance, compared to that of the straight square channel. The average measure of mixing uniformity for the coiled tube, as inferred from Figure 7a, can be up to four times better than that for a straight-channel T-junction. We note that the standard deviation at the T-junction (L = 0) is slightly different for various designs. This may be attributed to the effect of coiled design which, in turn, affects the mixing rate from the very beginning. The reaction rate for coiled designs is also improved significantly, compared to the straight channel (see Figures 7b and 7c); the conversion rate for coils can be up to 80% higher than that for the straight-channel T-junction. As shown in our previous work,1619 the design of the coils 1976



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Figure 7. Mixed mean values along channel for various channel configurations (a) mixing uniformity, (b) oxygen mass fraction for T-junction [—] and well-mixed inlet [• • •], (c) methane mass fraction for T-junction [—] and well-mixed inlet [• • •], and (d) temperature.

improves heat-transfer performance significantly. Here, the finding is also consistent with previous results, because the mixed mean temperature along the coiled channel is higher than that of the straight channel (see Figure 7d). This suggests that the coiled design is suitable for highly exothermic/endothermic reaction to control the desired environment temperature. Furthermore, in the region near the T-junction, where mixing of opposing streams occurs, we note that the conical spiral channel offers the best mixing, reaction, and heat-transfer performance, compared to other designs, followed by helical spiral and in-plane spiral; toward the near outlet region, the helical channel performs the best, followed by in-plane spiral and conical spiral. The higher mixing and reaction rate for helical channel is attributed to the higher secondary flow intensity (see Figure 4d); moreover, the constant curvature ratio of the design maintains a stable secondary flow development, compared to other designs. It has been shown that coiled tubes offer mixing and reaction enhancement. Now, to quantify the effect of mixing and reaction separately, we compare two different scenarios of channel with and without T-junction; that is ,with mixing and without mixing (both air and methane are assumed to be well-mixed). Figures 7b and 7c respectively show the oxygen and methane concentrations along the channel for well-mixed (see dotted line) and with mixing (line), respectively. Note that a lower concentration is observed for well-mixed cases, because reaction occurs more uniform and effective throughout the channel, because of its better stoichiometry. Moreover, we observe that the order for reaction effectiveness is similar to the case with mixing, i.e., helical, in-plane spiral, conical spiral, and straight channel. Clearly, this

indicates that the coiled tube offers a significant enhancement for both mixing and reaction rate. 4.3. Effect of Flow Rate. A further point of interest in this study is the effect of flow rate, because it is directly linked to the flow behavior and required pumping power. In this study, three different flow rates—corresponding to Re ≈ 100, 500, and 1000—are examined. Note that the velocities in the right and left inlets are prescribed to be the same, for comparison purposes. Figure 8 depicts the mixing and conversion rate along the helical spiral microchannel T-junction at various Re values. Interestingly, as can be seen in Figure 8a, the mixing performance decreases as the inlet flow rate increases, especially in the first 20 mm from the T-junction, and becomes asymptotic. Similarly, the conversion rate also increases as the Re value decreases (see Figure 8b). This indicates that the coils microchannel T-junction is more effective in low inlet Re applications. This is due to the fact that, in the microchannel, mass transport is dominated by the diffusion process; hence, longer residence time is necessary to drive more molecular diffusion between two fluids, which, in turn, improves the mixing and reaction performance. In general, there is always conflict between thermodynamics and kinetics. A high thermodynamics (mixing and reaction) efficiency is achieved at low kinetics (low flow rate), and vice versa. Hence, we need to balance these two factors to achieve optimum conditions. In order to keep the operating cost of the reactor low, it is of interest to keep the pressure drop at a minimum: a good microreactor design should be able to obtain high mixing and reaction rates, while keeping the pressure drop low. The coils design, as shown in Figure 9, requires a higher pressure drop to 1977



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Figure 10. Figure of merit (FoM) for various channel configurations and inlet Reynolds number (Re) values.

Figure 8. Mixed mean values along the channel for various inlet Re values: (a) mixing uniformity and (b) oxygen mass fraction.

Figure 9. Pressure drop required for various channel design at various inlet Re values.

drive the flow; this can be expected from the more-complex flow patterns inside the channel, because of the presence of secondary flow. Among all designs, the helical spiral channel requires the highest pressure drop, followed by in-plane spiral, conical spiral, and straight tube, which requires the least pumping power. The pressure drop increases with the flow rate (see Figure 9). Note that the pressure drop for the coiled base channel is ∼30%40% higher than that for the straight channel at low Re values (∼ 100); whereas, at Re values (∼1000), the pressure drop required for coils is much higher (up to twice), compared to that for the straight channel. The “Figure of Merit” concept is introduced to compare the effectiveness of the reactor designs per unit pumping power (see eq 20). Figure 10 shows the computed FoM for various channel designs at different Re values. It is found that, apart from the higher mixing and reaction rate, the coiled designs have significantly

Figure 11. Mixed mean values along the channel for various coil diameters: (a) mixing uniformity and (b) oxygen mass fraction.

lower FoM values than the straight channel. This is due to the higher pressure drop required for coiled channels. It is also noted that the FoM decreases as the Re value increases. Among the coils designs, the in-plane spiral channel yields the best FoM, followed by the conical spiral and the helical spiral channel. When designing microchannel T-junctions, however, careful balance and consideration must be given to the mixing, reaction, and heat-transfer performance. If the performance is of greater interest (e.g., for pharmaceutical processes or highly exothermic reactions), one can consider coiled base channel design, because of their heat- and mass-transport enhancement. However, if pumping power is the major constraint, the straight microchannel T-junction is recommended. 1978


Industrial & Engineering Chemistry Research 4.4. Effect of Coil Diameter. Section 4.1 showed that mixing and reaction performance for the conical spiral channel in the vicinity of the T-junction is higher than that in other designs; this is postulated to be due to the small coil diameter near the T-junction region. Therefore, it is of interest to investigate the effect of coil diameter to the mixing and reaction performance. In this study, we compared three different coil diameters (see Rh in Figure 2d) for a helical spiral channel—e.g., 6, 8 (base case), and 10 mm—since these channel designs have the highest mixing and conversion rate, compared to others. For comparison purposes, the total length for each diameter and other parameters are held constant. Proceeding to the mixing rate for various coil diameters, as illustrated in Figure 11a, it is found that reducing coil diameter improves the mixing performance slightly, especially in the region near the T-junction. The reason for this improvement is that, for smaller coil diameter, the centrifugal force is greater, which results in higher secondary flows. Smaller coil diameter not only improves the mixing rate, but also enhances the conversion rate (see Figure 11b). It is also noted that the conversion rate improves by ∼8% when the diameter is reduced from 10 mm to 6 mm. However, this also imposes a higher pressure drop (by ∼17%). In addition, a smaller coil diameter (Rh) also results in a longer helical coil, compared to a larger coil diameter, and vice versa, provided that the total length of the channel (L) is the same.

5. CONCLUDING REMARKS A computational study has been conducted to investigate the mixing, reaction and heat-transfer performance of microchannel T-junction fitted with coiled base channels, i.e., conical spiral, inplane spiral, and helical spiral, which are related to the straight microchannel T-junction. It was found that the coiled base channel design improves the mixing, reaction, and heat-transfer rate significantly. However, it also imposes a greater pressure drop. Among the several coils designs studied, the helical spiral channel provides the best mixing, reaction, and heat-transfer performance. For applications where the mixing, reaction, and heat-transfer performance are of paramount importance, e.g., in the pharmaceutical industry, the coiled base microchannel T-junction can be a desired choice. ’ AUTHOR INFORMATION Corresponding Author

*E-mail address: [email protected].

’ NOMENCLATURE Ar = pre-exponential factor Bi = bulk/solid species (mol) b0i = stoichiometric coefficient for bulk reactant b00i = stoichiometric coefficient for bulk product cp = specific heat (J kg1 K1) Di = diffusivity of species i (m s2) Er = activation energy for the reaction (J kmol1) Gi = gas species (mol) g0i = stoichiometric coefficient for gas reactant g00i = stoichiometric coefficient for gas product keff = effective thermal conductivity (W m1 K1) kf,r = reaction rate constant using the Arrhenius expression L = total length of the channel M = mean molecular mass

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m_ dep = net rate of mass deposition (kg) p = pressure (Pa) Q = volume flow rate (m3 s1) R = universal gas constant (J kg1 mol1 K1) Ri = reaction rate of species i (kg m3) s = coil spacing Si = surface-adsorbed/site species (mol) s0i = stoichiometric coefficient for site reactant s00i = stoichiometric coefficient for site product Stemp = heat released/absorbed due to reactions (W m3) T = temperature (K) u = velocity (m s1) w = channel width x = mole fraction Greek Symbols

βr = temperature exponent F = density (kg m3) μ = dynamic viscosity (Pa s1) R = rate of reaction r ηpump = pump efficiency ωi = mass fraction of species i Subscripts and Superscripts

b = bulk dep = deposition eff = effective g = gas i = species i r = wall surface reaction r s = solid/site temp = temperature

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Numerical Evaluation of Transport Phenomena in a T-junction

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